Da es in Powershell eine Implementation für REST gibt, muss man nicht den Umweg über den .NET WebClient gehen.
$json = @{
AuthorizationToken = "44xx44x444x44xxxxx4xxx444x444xx";
Body = "Body 12345....";
Title = "Titel der Nachricht";
Link = "https://www.google.de";
LinkTitle = "Google";
Source = "Powershell";
TimeToLive = "60"
} | ConvertTo-Json
$uri = "https://pushalot.com/api/sendmessage"
Invoke-RestMethod -Method Post -Uri $uri -ContentType "application/json" -Body $json